Question

A equação (x − 2) · (x − 4) − 3 = 0 tem raízes iguais a

Answer 1

As raízes da equação de 2º grau são, x'= 5 e x" = 1.

• Aplicando a distributiva entre os parênteses, temos:

$(x-2)(x-4)-3=0\\\\x\cdot x+x\cdot(-4)-2\cdot x-2\cdot(-4)-3=0\\\\x^2-4x-2x+8-3=0\\\\x^2-6x+5=0$

• Aplicando a fórmula de Bháskara, temos:

$\Delta=b^2-4ac\\\\\Delta=(-6)^2-4\cdot1\cdot5\\\\\Delta=36-20\\\\\Large\boxed{\Delta=16}\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-(-6)\pm\sqrt{16}}{2\cdot1}\\\\\Large\boxed{x=\dfrac{6\pm4}{2}}\\\\\\\boxed{\large\begin {array}{l}x'=\dfrac{6+4}{2}\\\\x'=\dfrac{10}{2}\\\\\Large\boxed{\boxed{x'=5}}\Huge\checkmark\end {array}}\quad\quad\boxed{\large\begin {array}{l}x"=\dfrac{6-4}{2}\\\\x"=\dfrac{2}{2}\\\\\Large\boxed{\boxed{x"=1}}\Huge\checkmark\end {array}}$

Portanto, as raízes da equação de 2º grau são, x'= 5 e x" = 1.

Quer saber mais: Acesse:

• https://brainly.com.br/tarefa/47399745

Bons estudos!